Camera-trapping data analysis
We used the camera trap data to develop detection matrices based on the
absence (= 0) and presence (= 1) of jaguar and each of the five prey
species selected. Each column on the recording sheet represented an
eight-day interval during which the cameras were active, and each row
represented a unique camera trap station; double stations were listed as
a single station. These detection histories were used to investigate the
spatial interactions between the jaguar and each of the main potential
prey detected in the co-occurrence modeling. The prey species included
in the analysis were Pecari tajacu , Cuniculus paca ,Dasyprocta punctata , Mazama temama , and Mazama
pandora . Prey species that did not present enough detections,Tayassu pecari and Dasypus novemcinctus , were excluded.
We used a single season, two-species model (MacKenzie et al .,
2004, 2006) with R-studio software and the R-presence library to
estimate occupation (co-occurrence) and detection (co-detection) for
each pair of species (jaguar and prey). The naive occupation, which
reflects the proportion of cameras detecting a species in relation to
the total number of cameras, is reported. Two population parameters,
occupancy and detection, were estimated, which provide an estimate of
the proportion of an area occupied by a species.
We established the jaguar as the dominant species (A) and prey (B) as
the subordinate species and adopted the eight model parameters proposed
by Richmond et al . (2010). For occupancy (psi or Ψ): 1) ΨA -
probability of occupancy for species A; 2) ΨBA - probability of
occupancy for species B if species A is present; 3) ΨBa - probability of
occupancy for species B if species A is absent, and for detection (r or
ɣ), 4) pA - probability of detection for species A if species B is
absent; 5) pB - probability of detection for species B if species A is
absent; 6) rA probability of detection for species A if both species are
present; 7) rBA - probability of detection for species B if species A
was detected and both species are present; and 8) rBa - probability of
detection for species B if species A was not detected and both species
are present. If species occur independently, that is, the occupation of
one species does not depend on the other, then ΨBA = ΨBa. Similarly,
detection of one species relative to the presence or absence of another
can be determined; if the detection of the species occurs independently,
then rBA = rBa. We also used the interaction factor (SIF) which
indicates if the species of interest occur independently. The parameter
nu (N), which is the occupation probability estimate
(B|A)/probability (B|a), indicates if the jaguar and
the prey species use the sites independently, and the parameter rho (P),
which is the detection probability (rBA /probability rBa), indicates if
the detection of the predator affects the detection of a prey since they
both occupy a site. Nu and rho (SIF) values that equal one suggest
species occur independently, but SIF values <1 suggest species
coexist less frequently than if they were distributed independently
(avoidance among the pair of species analyzed) and SIF values
>1 suggest a tendency for species to occur more frequently
than if they were distributed independently.
We used the Akaike model selection criterion (Akaike, 1973) to identify
which of the three models (below) that best describes the data on the
joint occurrence of each pair of species and assigned the following
variable definitions: SP is the effect of the species; INT is the effect
of the interaction on the presence of species B whether species A is
present or not; INT_o is the detection level interaction when the
occupation of one species changes the probability of detection of the
other species; and INT_d, is the detection level interaction where the
detection of one species changes the probability of detection of the
other species on the same occasion of the sampling (i.e., eight-day
period).
• Model 1: psi~SP + INT,
p~SP + INT_o + SP:INT_o + INT_d [psi (SP P
INT) p (SP P INT_o P SP T INT_o P INT_d)]. This is the most
complete model with three parameters for occupancy (psi) and five
parameters for detection. It assumes the probability of occupancy
depends on the occupancy of A and the probability of occupancy of BA
because ΨBA = ΨBa. It also assumes
that detection depends on pA, rA, pB, rBA and rBa.
• Model 2: psi~SP,
p~SP + INT_o + INT_d + SP:INT_o psi (SP) p (SP P
INT_o P INT_d P SP T INT_o). Occupancy depends only on the species,
and unlike model 1, assumes that species occupancy is independent. This
implies ΨBA = ΨBa and is represented
by the absence in the adjustment of the interaction term in the
occupancy.
• Model 3: psi~SP + INT,
p~SP + INT_o + SP:INT_o psi (SP P INT) p (SP P INT_o
P SP T INT_o). Unlike model 1, it assumes that detection probabilities
of species B do not depend on the detection of species A (i.e.,
rBA = rBa ).